You need to time yourself. Give yourself a 5-min break every 30 mins. Walk around, stretch, do some pushups. Work in a nice clean environment, so you won't get distracted. Stay off the computer and phone whenever possible.

Thanks. I haven't seen any techniques for simplifying that form, but would you mind explaining a little bit on what you mean by applying a product of sines and cosines? I'm not sure if I learned that yet, but I'm willing to learn now.

I got -399.567sinθ-13.369sin13.369θ for x' and 339.567cosθ+13.369cos13.369θ for y'. I'm sorry, but I fail to see how that trig identity would help, since both coefficients are different and I have cos13.369θ, not a regular cosθ.